Pogba has been nursing an ankle injury and has not played for the Premier League club since its 1-1 home draw against Arsenal at the end of September, Reuters reported.
Solskjaer said the 26-year-old would not be fit for Sunday’s home clash against Aston Villa but the Frenchman could return to the side when it hosts Jose Mourinho’s Tottenham Hotspur on December 4.
“Sunday, no,” Solskjaer told reporters when asked about Pogba’s return.
“Spurs? I can’t say now, because I’ve not been home and seen him, let’s see where he’s at when he comes back and starts training with us.
“Every player is allowed to be injured when he’s injured and Paul is working hard to get back. No one can doubt his professionalism, his willingness or his desire to play football.
“He’s one of the best midfielders in the world and it’ll be like signing a new player before the transfer window opens... He’s stepping up his recovery and let’s see how soon he’ll be match-fit and available.”
Midfielder Scott McTominay could also return against Villa after missing United’s last two games with an ankle injury and the Norwegian boss said that would allow Pogba to play in a more advanced role when he returned to the side.
“We hope Scotty will be back as soon as possible,” Solskjaer added. “Maybe Villa, maybe Spurs, hopefully for Sunday.
“The beauty we have with Paul is that he can play in so many roles. He can play in a (midfield) two, he can play in a three and he can play as a No.10... Jesse (Lingard) is also coming back to his best.
“We’ve got more and more coming back and that’s great. We shall see who is fit when Paul is fit because you can’t plan too far ahead in football.”